Norm
Dee. 5, 39.54 activation would be expected to be greater for 111, both because the free energy of activation is greater and because of the postulated additional strain in the transition state. However, this result was not expected for the five-membered ring 11. A consideration of the relative entropies of activation for the three compounds shows that i t is the very large relative entropy of activation for 11 which overwhelms the effect of the increased heat of activation and causes I1 to react faster than the straight-chain compound I. The entropy of activation for I11 is also greater than that for the standard compound I , but in this case the heat of activation predominates so that I11 reacts more slowly than I. The high entropies of activation probably indicate that in this reaction compounds I1 and I11 have greater freedom of motion and a larger number of degrees of freedom in their transitions states than in the ground states. It would be of interest to compare these results with those for a reaction of ordinary carbocyclic rings, proceeding by a bimolecular displacement mechanism, but apparently no such study has been published. Some experiments were also carried out to determine rates of hydrolysis of linear and cyclic difunctional silanes (R2SiH2). Theoretically i t should be possible to determine the rates of hydrolysis of each of the two hydrogen atoms by a process entirely analogous to that used in radiochemistry to analyze curves representing two
6017
simultaneous first-order decay reactions. In practice, however, i t was found that the first hydrogen is removed so rapidly that no estimate of the rate could be made. Approximate rates were obtained for the removal of the second hydrogen atom. The reactivity of the compounds tested decreased in the order
7
/-\ SiH2 > (n-C3H7)&iH2> /-SiH2 -/ L/ L/ The order is thus the same as that observed with the monofunctional cyclic silanes. It is interesting that the order of reactivity of cyclic silanes as a function of ring size follows the same order observed for carbocyclic compounds in several different If the assumptions made above about the conformations of silicon-containing rings are valid, then these experiments provide additional confirmation of the I-strain theory'-3 and indicate that it may be extended to reactions occurring a t elements other than carbon. In any case, i t seems that the factors which operate to cause activation and deactivation of carbocyclic rings of certain sizes also operate to cause quite similar effects among cyclic organosilicon compounds. Acknowledgments.-The author is grateful to Dr. Eugene G. Rochow for many helpful discussions, and to the National Science Foundation and the Mallinckrodt Fund for financial support. SiHz > I
CAMBRIDGE, MASS
NOTES Thermodynamic Functions of the Chlorofluoromethanes BY L. F. ALBRIGHT, W. C. GALEGAR AND E;.K. INNES RECEIVED AUGUST11, 1954
Two recent studies of chlorofluoromethanes have made it possible to refine the thermodynamic calculations by Gelles and Pitzerl for these compounds. Claassen2 combined his measurements of the Raman spectra of the gases with the infrared data of Plyler and Benedict3 to estimate what he considers to be the best values of the fundamental frequencies. Thirteen of the frequencies, whose values are less than 800 cm.-l, differ by more than ti em.-' and four by greater than 20 em.-' from the values reported by Plyler and Benedict and used by Gelles and Pitzer. Masi4 measured the heat capacity of gaseous CC12R and reported derived values for the ideal gas, which he claims are accurate to within 0.15% a t temperatures from -30 t o 90". His results are about 0.7% higher than values calculated using the rigid-rotator, (1) E. Gelles and K. S. Pitzer, THISJOURNAL, 75, 5259 (1953). (2) H . H. Claassen, J . Chem. Phys., 99, 50 (1954). (3) E. K. Plyler and W. S. Benedict, J . Research Nad. Bur. Standards, 47, 202 (1951). (4) J. F . Masi, THIS JOURNAL, 74, 4738 (1952).
harmonic-oscillator approximation. The difference was attributed to a shift of one frequency (later verified by Claassen2) and to the effect of anharmonicity. Masi included approximate values for the anharmonicity contribution. These values became appreciable a t higher temperatures. McCullough and co-workers5 have presented empirical equations for correlating anharmonicity contributions for various thermodynamic functions. These equations are used in the present study. The thermodynamic functions of chlorofluoromethanes were calculated assuming a rigid-rotator and harmonic-oscillator in the usual manner a t temperatures from 100 to 1000°K. Calculations were made using the products of the moments of inertia presented by Gelles and Pitzer,' fundamental frequencies given by Claassen,2 and tables of the vibrational contributions to various thermodynamic functions as presented by Taylor and Glasstone.6 The experimental heat capacity values for CC12F2 were subtracted from the calculated ones. The differences were assumed to be caused by anhar(5) J. P. McCullough, H. L . Finke, W. N. Hubbard, W. D. Good, R. E. Pennington, J. F. Messerly and G. Waddington, ibid., 76, 2661 (1954). (6) H. S. Tavlor and S . Glasstone, "A Treatise on Physical Chemistry," Vol. I, D. Van Nostrand Co., New York, N . Y.,1942, p. 055.
monicity and were correlated by the equation5 C"(anh) = z ( C O I R ) [ [ 3 ( C o / R ) / U l [1 2/U1[(ff0
+
- Hi')/R77 J
to obtain the constants z = 0.1573 and p = 300 cm.-1 in U = hcv/kT. Here, C"/R and (H" H,")/RT are values for the harmonic oscillator whose frequency is p , At the suggestion of Dr. D. W. Scott,' z was assumed to be the same for all five chlorofluoromethanes and a proportionality constant was assumed between v and the sums of the fundamental frequencies. Using values of v determined in this manner and equations5 for So(anh) and (Bo- H$)/T(anh), anharmonicity contributions were calculated over the desired TABLE I THERMODYNAMIC PROPERTIES O F T , OK.
e;
100 150 200 250 300 400 500 600 700 800 900 1000
11.36 14.44 16.79 18.62 20.08 22.04 23.28 24.07 24.61 25.00 25.28 25.52
-Ha/
(He
T
8.85 10.23 11.59 12.81 13.91 15.71 17.10 18.2% 19.08 19.80 20.40 20.90
T,OK.
c;
100 150 200 250 300 400 500 600 700 800 900 1000
10.37 13.15 15.46 17.31 18.81 20.99 22.43 23.35 24.01 24.49 24.87 25.16
T
c;
T
T
8.54 9.63 10.80 11.92 12.95 14.71 16.12 17.25 18.19 18.94 19.58 20.12
49.91 53.57 56.49 59.03 61.30 65.27 68.72 71.76 74.50 76.96 79.24 81.37
100 150 200 250 300 400 500 600 700 800 900 1000
9.49 11.83 14.05 15.90 17.45 19.81 21.44 22.58 23.38 23.97 24.41 24.74
-T HoO)/
8.28 9.06 10.05 11.04 11.98 13.66 15.07 16.23 17.20 18.02 18.70 19.30
-(FO
8.80 10.69 12.71 14.53 16.13 18.66 20.49 21.79 22.73 23.42 23.94 24.35
(H'
57.04 62.27 66.75 70.70 74.25 80.29 85.33 89. 68 93.41 96.72 99.73 102.38
58.45 63.20 67.29 70.95 74.25 79.98 84.84 89.01 92.69 95.90 98.82 101.49
- Hoe)/
T
S O
49.36 52.85 55.59 57.95 60.04 63.72 66.93 69.78 72.36 74.72 76.87 78.80
57.64 61.91 64.65 68.99 72.02 77.38 82.00 86.01 89.56 92.74 95.57 98.19
(7) D W.Scott, private communication. 1954
T
--(Fa - H;)/
T 47.18 50.57 53.15 55.34 57.28 60.70 63.69 66.35 68.78 71.02 73.05 74.98
SO
55.29 59.20 62.56 65.60 68.38 73.38 77.78 81.61 85.05 88.12 90.89 93.46
-
T , OK.
c;
(H" HoO)/ T
100 150 200 250 300 400 500 600 700 800 900 1000
8.31 9.61 11.37 13.11 14.73 17.41 19.43 20.91 21.99 22 84 23 42 23.91
8.00 8.30 8.84 9.52 10.26 11.72 13.08 14.26 15.29 16.19 16.96 17.64
- Hi)/ T 42.75 46.04 48.50 50.54 ,52.34 55.49 58.26 60.76 63.03 65.13 67.09 68.89
-(FO
SO
50.75 54.34 57.34 60.06 62.60 67.21 71.34 75.02 78.32 81.32 84.05 86.53
TABLE VI ANHARMONIC CONTRIBUTION TO HEAT CAPACITY S O
-~
- Hf)/
8.11 8.63 9.41 10.26 11.10 12.68 14.09 15.26 16.27 17.10 17.84 18.48
S O
48.19 52.03 55.16 57.89 60.34 64.58 68.23 71.46 74.33 76.92 79.33 81.48
- Ht)/ -(Fo - HoO)/
( H O
G
TABLE V THERMODYNAMIC PROPERTIES OF CFd
TABLE I11 THERMODYNAMIC PROPERTIES OF CCLS T,OK.
T,OK. 100 150 200 250 300 400 500 600 700 700 900 1000
- Hi)/
-(F"
TABLE I1 THERMODYNAMIC PROPERTIES OF CCLF (Ha
TABLE IV THERMODYNAMIC PROPERTIES OF CClF,
T , "K.
CClr
CCIJF
CClrF,
CClFz
CFk
100 150 200 250 300 400 500 600 700 800 900 1000
0.02 .05 .08 .ll .14 .20 .25 .30 .35 .40 .45 .50
0 01 .03 .06 .09 .ll .16 .21 .25 .29 .34 .38 .43
0.01 .03 .05 .07 .09 .13 .17 .21 .25 .29 .33 .36
0.00 .01 .03 .05 .08
0.00 .01 .03 .04 .06 .09 .13 .16 .19 .22 .25 .28
.11 .15 .19 .22 .25 .28 .32
temperature range. These contributions were added to those of the harmonic-oscillator approximation with the results shown in Tables I-V. The heat capacity values due to anharmonicity are shown in Table VI. The calculated results based only on the harmonic-oscillator approximation vary in all cases by less than 0.18 cal./deg. mole and in most cases by less than 0.10 cal./deg. mole from the values presented by Gelles and Pitzer.' The anharmonicity contributions become appreciable a t higher temperatures so that the total values of the various thermodynamic functions differ in such cases by as much as 0.2 to 0.5 cal./deg. mole. The experimental entropy values available for these compounds are all for low temperatures. Within experimental accuracy the comparison with cal-
Uec. 5, 1954
NOTES
culated values that was made by Gelles and Pitzer' is unaffected. The anharmonicity calculations are considered to be only approximations. Until more specific heat data and/or anharmonicity constants are experimentally determined, further significant refinements of anharmonicity contributions seem impossible. We would like t o thank Professor J. R. Nielsen of the University of Oklahoma, Dr. D. W. Scott of the Bureau of Mines, Professor W. H. Stockmayer of Massachusetts Institute of Technology and Dr. J. F. Masi of the Callery Chemical Company for advice and suggestions.
assembly was then heated in a furnace provided with silicon carbide heating elements for 24 hours a t 1250'. On removal from the furnace, a piece of the sintered mass was cut off for the preparation of specimens for the dilatometer. The remainder was washed repeatedly with hot water to remove the flux. A second set of interferometer specimens was then prepared from this material and was further treated successively with boiling water, hydrochloric acid, ammonium hydroxide and boiling water, and was then carefully dried. Analysis showed 98.7% silica and examination under the petrographic microscope indicated complete conversion to tridymite. The residual mass was ground in an agate mortar to pass through a 400-mesh screen and was given the same series of washings as before. I t was this finely ground material which was used by Anderson3 and by Mosesman and Pitzer in their specific heat measurements. Another sample was prepared by heating the purified quartz and sodium tungstate in the same proportions for 27 hours a t 1300". The cooled sinter was boiled in 1: 1 HC1 for 2 hours, was left overnight in a constant-boiling mixture of HCl, was then repeatedly washed in boiling distilled water and was finally dried. Specimens for the dilatometer were then prepared from the dried material. Examination under the microscope showed complete conversion to tridymite. A fourth set of specimens was cut from the center of a silica coke-oven liner which, as a result of long service at high temperature, had been converted almost completely to tridymite. This liner has been described elsewhere.' Apparatus.-The measurements were made by means of an interferometric dilatometer which has already been described.6 The specimens for each sample were in the form of three small pyramids, about 3 mm. in height, which were placed between the silica plates of the interferometer. The observations were plotted on a large scale as increase in length per unit length against temperature. Since these measurements were made with the temperature increasing a t a constant rate of 3" per minute, and since the specimens were not good thermal conductors and, moreover, were not of identical shape, there were inevitably small temperature differences among them. The evidence indicates that this difference was usually less than 0.3'. The specimens therefore transformed in succession a t intervals of a few seconds, rather than simultaneously. This made it difficult to obtain precise measurements within a degree or so of the transition temperatures, with the result that the several length-temperature curves did not coincide but were displaced relative to each other. There was, however, substantial agreement in the slope of the curves, as read from the plot by means of an optical tangent meter. Accordingly, the results are reported in the form of instantaneous coefficients as a function of temperature.
SCHOOL OF CHEMICAL ENGINEERING OF CHEMISTRY DEPARTMENT UNIV.OF OKLAHOMA NORMAN, OKLA.
The Coe5cient of Linear Thermal Expansion of Tridymite BY J. B. AUSTIN RECEIVED JUNE 9, 1954
The occurrence of two "high-low" inversions in tridymite is well-established and the inversion temperatures have generally been accepted as close to 117 and 163") respectively,' although there have been occasional suggestions that these temperatures may vary significantly. Mosesman and Pitzer, * however, have reported heat content data which indicate the possible existence of a third transition a t 223". Since this transition had not been described previously, and since they were unable to explain i t on the basis of possible impurities present in their sample or to interpret i t in terms of present knowledge of the crystalline structure of tridymite, they suggested that final acceptance should await further verification. As such transitions are usually accompanied by a change in volume, measurements of thermal expansion offer a possible means of confirmation. Accordingly, a number of measurements of linear expansion, made some years ago during a study of the behavior of silica refractories, have been reexamined for indications of this third transition. Samples.-Three different samples of silica were examined. Two were purified tridymite, one being the same material used by Mosesman and Pitzer. The third was a silica coke-oven liner which, after long service, had been converted almost entirely to tridymite. The raw material for the purified tridymite was, in each case, a very pure sample of vein quartz from Lake Toxaway, North Carolina. This material was ground to pass a 60mesh sieve, was repeatedly washed with hydrochloric acid, and then dried. Analysis with hydrofluoric acid gave 99.9QyoSios. The residue, when tested with sodium thiocyanate; gave a red coloration indicating the presence of iron. For the first preparation, this purified quartz was mixed with purified sodium tungstate in the proportion of 6 silica to 1 NasWO4 by weight. The mixture was ground in an agate mortar t o pass 200-mesh screen. It was then placed in a platinum cone, which was covered with platinum foil resting on two porcelain rods, set in a magnesia block into which a noble metal thermocouple had been inserted. This (1) R. B. Sosman, "The Properties of Silica," Chemical Catalog Co.. New York, N. Y., 1927, pp. 124, 125. (2) A. hrosesman and K. S. Pitzer, THISJOURNAL, 63, 2348 (1941).
(io19
Results The composite data for all three types of specimen are presented in Fig. 1. For all specimens, the values of the coefficient, a t or just above room terne perature, clustered in the range 23 to 26 X 10-8, and then increased sharply to the inversion temperature. In all specimens, the first inversion appeared to he complete within a degree of 117". The coefficient for the intermediate form was, for all specimens, close to 45 X lop6, and again increased rapidly as the inversion temperature was approached. The second inversion appeared to be complete within a degree of 163". Above the second transition, the coefficient for each set of samples was, within the error of measurement, constant over the range 163 to 210". There was, however, some variation in the magnitude of the coefficient in this range. Thus, the specimens cut from the coke-oven brick gave 45 X and a second run on the sample which still whereas for five contained the flux gave 65 X (3) C.T. Anderson, i b i d . , 8.3, 568 (1936). (4) J. B. Austin and R . H. H. Pierce, J . Anter. Ceramic SOC,16, 102 (1933) ( 5 ) J . B. Austin and R . €1. H. Pierce, THIS JOUYNAL. 65, G61 (1933).
